Znorg. Chem. 1980, 19, 1307-1314 Another measure of the covalent/ionic nature of the complexes can be found in the gross atomic charge assigned to the metal and ligand, as shown in Table IV. This is equivalent to a Mulliken population analysis in the LCAO scheme. The pattern obtained here is different from that discussed previously considering only the f orbitals. Clearly, NpF6 is the most covalent, but PaF62- appears more covalent than UF6-. However, if the bonding is mainly ionic, then these results are consistent; i.e., the greater the charge on the complex as a whole the smaller the charge on the central ion. Since the F ion is the smallest and least polarizable halide ion, an overall charge on the complex will result in more charge being placed
1307
on the central metal ion. There appears to be little difference for the other halide ions. Summary This paper has described a systematic study of the 5f ligand field splitting in the 5f' complexes PatVX?-, uvx6-( X = F, C1, Br, I), and NpV'F6. A quasi-relativistic MS X a routine was used for this purpose. The trends observed in the f-orbital ligand field splitting appear to be principally ionic. Registry No. PaFs2-, 49864-66-6; PaCls2-, 44463-14-1; PaBrs2-, 44463-09-4; PaI:-, 44463-23-2; UF,-, 73017-47-7; UCl,, 44491-58-9; UBr,, 44491-06-7; UI6-, 73002-73-0; NpF6, 14521-05-2.
Contribution from the Department of Chemistry, University of Edinburgh, Edinburgh, EH9 355 Scotland, and the Inorganic Chemistry Department, University of Oxford, Oxford, OX1 3QR England
Electronic Structure of the Sulfur Nitrides. Ab Initio Calculations and Photoelectron Spectra R. H. FINDLAY, M. H. PALMER,* A. J. DOWNS, R. G. EGDELL, and R. EVANS
Received June 7, 1979 Ab initio molecular orbital calculations of better than double-l quality are reported for SN, S2N2,S4N4,and a number of open-shell cationic states; midbond functions (on all molecules) and polarization functions on S2N2are included. The gas-phase UV-photoelectron spectra (PES) up to 25 eV have been investigated and assigned on the basis of the calculations and cross-section changes under He I/He I1 irradiation. The electronic structures of S2N2and S4N4were investigated by transformation of the wave functions to a localized bond basis. A significant amount of S-S bonding was calculated for S4N4but no N-N bonding. Across ring bonding was absent from S2N2.
Introduction The long-known series of sulfur nitrides (NS),, where x = 1-4, have been widely investigated' and contrast sharply with the corresponding series (NO), with x = 1, 2, 3, and 4 where only the first is well-known. Particular impetus to the study of the NS series has been provided by the remarkable electronic properties of the chain-type metallic conductor (SN),? Tetrasulfur tetranitride, S4N4 (l), is perhaps the most
of alternating S and N atoms and is essentially quar re;^ it is the usual precursor for polymeric (SN),. In the present work we discuss the electronic structures of (a) S2N2and (b) S4N4,both at their known crystal structure g e ~ m e t r i e sand , ~ ~ (c) ~ SN, at the microwave g e ~ m e t r y to,~ gether with a number of open shell cationic states, for which the geometry is assumed to be the same as the ground state. The actual dimensions used were S N = 1.4957 A, S N = 1.657 8, and SNS = 90.42O in S2N2,and S N = 1.616 A and NSN = 104.5' in S4N4(D2J. We assume that the molecular structures of the crystalline solids are still relevant to the gaseous SzN2and S4N4molecules; the similarity of the vibrational spectrum of S2N2in the solid and gas phases supports this assumption. A number of previous electronic structure calculations have been reported for the present series of molecules: (a) for SN and/or SN+ X a 6 and ab initio (i) STO-3G,' (ii) extended basis,8s9 and (iii) uhf;1° (b) for S2N2CNDO-2,"J2 CNDO-S,13 INDO (trip-
W
W
~~
1
well-known member of the series, the molecular structures being based on a square-planar array of nitrogen atoms inserted within a approximately tetrahedral quartet of bridging sulfur atom.3 The dimer, disulfur dinitride SzNz(2), consists
2
*Towhom correspondenceshould be addressed at the University of Edinburgh. 0020-1669/80/1319-1307$01.00/0
~~~
(1) Banister, A. J. MTPInt. Rev. Sci.: Inorg. Chem., Ser. Two 1975, 3,41. (2) Greene, R.L; Street, G.B. Chem. Phys. One Dimensional Met. Proc. NATO Adu. Study Inst. 1976, 1 . Geserich, H. P.; Pintschovius, L. Festkorperprobleme, 1976, 16, 65. (3) Sharma, B. D.; Donohue, J. Acta Crystallogr. 1963, 16, 891. (4) (a) MacDiarmid, A. G.; Mikulski, C. M; Russo, P. J.; Saran, M. S.; Garito, A. F.; Heeger, A. J. J. Chem. SOC.Chem. Commun. 1975,476. (b) Mikulski, C. M.; Russo, P. J.; Saran, M. S.; MacDiarmid, A. G.; Garito, A. F.; Heeger, A. J. J . Am. Chem. SOC.1975, 97, 6358. (c) Cohen, M. J.; Garito, A. F.; Heeger, A. J.; MacDiarmid, A. G.;Mikulski, C. M.; Saran, M. S.; Kleppinger, J. Ibid. 1976, 98, 3844. (5) Zeeman, P. B. Can J . Phys. 1951, 29, 174. (6) Salahub, D. R.;Messmer, R. P. J. Chem. Phys. 1976, 64, 2039. (7) Deutsch, P. W.; Curtiss, L. A. Chem. Phys. Lett. 1977, 51, 125. (8) OHare, P. A. G.J . Chem. Phys. 1970,52, 2992. (9) Jafri, J. A,; Newton, M. D.; Pakkanen, T. A.; Whitten, J. L. J . Chem. Phys. 1977,66, 5167. (10) Tarok, F.; Pulay, P.; Szondy, T.; Nagy, P. Acra Chim. Acad. Sci. Hung. 1974, 80, 139. (11) Adkins, R. R.;Turner, A. G. J . A m . Chem. SOC.1978, 100, 1383. Adkins, R. R.;Dell, R.;Turner, A. G.; J . Mol. Struct. 1976, 31, 403. (12) Kertesz, M.; Suhai, S.; Azman. A.; Kocjan, D.; Kiss, A. I. Chem. Phys. Lett. 1976, 44, 53. (13) Salanek, W. R.;Lin, J. W-p.; Paton, A.; Duke, C. B.; Ceasar, G.P. Phys. Rev. B. 1976, 13, 4517.
0 1980 American Chemical Society
1308 Inorganic Chemistry, Vol. 19, No. 5, I980
Findlay et al.
I
eV
Figure 1. (a) He I and (b) He I1 PE spectra of S2Nz.
let),I4 extended €luckel (EH),12 X q 6 and ab initio (i) STO3G,7J2J5(ii) extended b a s i ~ , and ~ J ~(iii) configuration intera ~ t i o n(c) ; ~ for S4N4CNDO-2,I6 CNDO-BW,I7CNDO-S,13 EH,I8J9and XaS6The present work is the first ab initio study with the same large basis sets for all three molecules such that the results can be compared. The gas-phase He I photoelectron spectrum (UPS) of S2N?0 and S4N4in the region 9-12 eVI3 have been confirmed and extended to the He I1 region; X-ray photoelectron spectra (XPS) have also been reported earlier for solid S2N221 and S4N4.13 Computational Methods A linear combination of Gaussian orbital basis (LCGO) was used. Two main bases were used: (i) a medium-size minimum basis N (7s 3p), S (10s 6p Id) scaled to optimize exponents in the N S bond as previously**and (ii) a new contractionz3of the S (12s 9p) and N (9s 5p) bases by Dunning24and Veillard.25 These final contractions are better than double p (with for example S [7s 2pl) and were further augmented for the individual compounds, the limiting factor being a program limitation to 126 basis functions. SN was augmented by an sp basis of midbond functions and 3ds, S2N2by these plus an sp ring center and 3dN,and S4N4by s-functions midbond (S-S and S-N). Thus the largest S4N4 calculation used 126 basis functions and generated 10 magnetic tapes of integrals (2400 ft/1600 bpi), and the SCF took 200 @eration on a CDC-7600; the largest bases for SzN2 and SN were 102 and 45, respectively. Total energies (all basis sets) and orbital energies (restricted to the valence shells of the molecules and including only selected calculations) are given in Tables I and 11.
Experimental and Instrumental Methods S4N4was prepared by the reaction between ammonia and S4N3C1 suspended in CC1,.z6~z7 Following removal of the solvent in vacuo, Yamabe, T.; Tanaka, K.; Fukui, K.; Kato, H. J . Phys. Chem. 1977,81, 727. Collins, M. P. S.;Duke B. J. J . Chem. SOC.,Chem. Commun. 1976,701. Cassoux, P.; Labarre, J.-F.; Glemser, 0.; Koch, W. J. Mol. Struct. 1972, 13, 405. Gopinathan, M. S.; Whitehead, M. A. Can. J . Chem. 1975, 53, 1343. Gleiter, R. J . Chem. Soc. A 1970, 3174. Turner, A. G.; Mortimer, F. S. Inorg. Chem. 1966, 5, 906. Frost, D. C.; Le Geyt, M. R.; Paddock, N. L; Westwood, N. P. C. J . Chem. Soc., Chem. Commun. 1977, 217. Sharma, J.; Downs, D. S.; Iqbal, Z.; Owens, F. J. J . Chem. Phys. 1977, 67, 3045. Palmer, M. H.; Findlay, R. H. J. Chem. SOC.,Perkin Trans. 2 1974, 1885; Palmer, M. H.; Gaskell, A. J.; Findlay, R. H.; Kennedy, S. M. F.; Nisbet, J. D. “Quantum Chemistry-The State of the Art, April 1974”; Saunders, V. R., Brown, J., Eds.; Science Research Council, London; 1975. Redshaw, M.; Palmer, M. H.; Findlay, R. H. 2. Naturforsch. A 1979, 34, 220. Dunning, T. J . Chem. Phys. 1970, 53, 2823. Veillard, A. Theor. Chim. Acta 1968 12, 405. Becke-Goehring, M.; Latscha, H. P. Z. Anorg. Allg. Chem. 1964, 333, 181.
8
12
16
eV
20
24
Figure 2. (a) He I and (b) He I1 PE spectra of S4N4.
’I
7
-.
I P
E
, A,
20
, I
Figure 3. Orbital energies by symmetry and assignment for SzNz: (a) for semiempirical (1) CNDO-2, (2) CNDO-S, and (3) Xa;(b) for ab initio (4) Collins and Duke,I5 ( 5 ) minimal sp (present work), (6) minimal spd, (7) Jafri et al., and (8) largest basis (present work). the crude product was recrystallized from benzene. The S4N3C1was itself obtained by the method of Jolly et aLZs This involves reaction between NH4C1and S,Cl2 to produce S3N2Cl,which was then allowed to interact with further SzCl, to yield the desired product. S2Nzwas generated by pyrolysis of S4N4vapor over silver W O O I , ~ ~ a process accomplished in a two-stage furnace attached to the volatile inlet probe of the spectrometer. The temperatures of the two furnace zones were adjusted to optimize counts from the product S2Nzwithout pronounced contamination of the spectrum by Nz. PE spectra were measured on a Perkin-Elmer PS 16/18 spectrometer modified for He I1 measurements by the inclusion of a hollow-cathode discharge lamp and high-current power supply (Helectros Developments). Spectra were accumulated in a 5 12-channel multiscalar (Bentham Instruments Ltd.), analyzer voltages being swept by reference to a linear ramp produced by a D/A converter receiving channel address pulses from the scalar. (27) Evans, R. unpublished work. (28) Jolly, W. L; Maguire, K. D.; Rabinowitch, D. Inorg. Chem. 1963, 2, 1304. (29) Becke-Goehring, M. Inorg. Synth. 1960, 6, 123.
Inorganic Chemistry, Vol. 19, No. 5, 1980 1309
Electronic Structure of the Sulfur Nitrides Table I. Molecular Total Energies (au) for the Molecules as a Function of Basis Set
SN ET V/T
SP
SPd
-451.833 59 -1.999 16
-451.892 13 -1.999 87
sp
+ midbond (sp)
spd
-451.905 14 -2.000 24
+ midbond (sp)
-451.910 65 -2.000 26
SN+ ~~
~
double c
ET VIT
SP
SPd
sp + midbond (sp)
-451.484 I9 -2.000 07
-451.556 I 9 -2.000 79
-451.574 26 -2.001 19
spd
+ midbond (sp)
-451.519 40 -2.001 19
S, N,
double f spd
ET VIT
+ midbond +
minimal spd
SP
SPd
center
-902.023 02
-903.593 90 -1.998 87
-903.785 96 -1.999 99
-903.842 75 -2.000 59
spd + midbond center + pol
+
-903.859 92 -2.000 42
S4N4
double 5
minimal
ET VlT
SP
SPd
SP
sp + midbond
-1803.272 60 1.960 1
-1804.0827 -1.9622
-1807.140 78 -1.998 51
-1807.384 09 -1.999 52
Spectra were calibrated by reference to signals due to admixed nitrogen and helium ionizations. PE spectra are shown in Figure 1 and 2, while ionization energy data are collected in Tables I11 and IV. The final correlations of the spectral and calculated data (using either Koopmans' theorem or open-shell calculations) are shown in Figures 3 and 4 and Tables I and 11. Principal Results and Spectral Assignments SN. Shown in Tables I and I1 are results derived from the spin-restricted Hartree-Fock (RHF) calculations for the ground configuration 1a22a23a24a21a45a26a27a22a43a1, together with the results of unrestricted (UHF) calculations. The single occupancy of the 3a subshell leads to nondegeneracy of the la and 2a (axand ay)levels in the lowest energy state. If these are constrained to be degenerate, the total energy is raised by ca. 0.013 au. The lowest RHF total energies we have calculated for SN and SN' (Table I) are very similar to those of O'Hare (-45 1.932 86 and -45 1 S 7 4 63 au, respectively)8 or TBrok et al.,1° our values for the orbital energies follow the same symmetry sequence in energy for both the small and the largest calculations. For both NS and NS' the energy lowering on addition of midbond sp functions is about the same as the addition of 3d to S (0.08 au). The nature of the lowering is however quite different in view of the different geometric positioning. The dipole moment of SN, the only member of the present series to possess one, is very sensitive to basis set (cf. ref 8 also); addition of 3ds and midbond functions leads to marked increases from the sp result (1.38 D) (which is near to that of Torok et al.1° at their best energy) to 1.75 D which is close both to that of O'Hare (1.73 D) and to the experimental spectral value of 1.86 D;30it is interesting to note that O'Hare's wave function for SN appears to have more d functions on N than S, contrary to normal practice. The full photoelectron spectrum of SN has not yet been reported, but a recent UV-PES value for the first IP is 8.87 eV,31to be compared with an earlier value of 9.85 eV8 on the (30) Amano, T.; Saito, S.; Hirota, E. J . Mol. Spectrosc. 1969, 32, 97. Carrington, A.; Howard, B. J.; Levy, D. H.: Robertson, J. C. Mol. Phys. 1968, IS, 187. Revision in: Byfleet, C. R.;Carrington, A,; Russell, D. K. Ibid. 1971, 20, 271.
'1 I
I P
90
Figure 4. Orbital energies by symmetry and assignments for S4N4: (a) for semiempirical (1) extended Huckel, (2) CNDO-S, and (3) XCY;(b) for ab initio (present work) (4) minimal sp, (5) minimal spd, (6) double l sp, and (7) double { sp + midbond ( S / S , S-N).
basis of electron-impact data. The present minimal basis set calculations yield 11.09 and 9.75 eV by using Koopman's theorem and the ASCF (IP = EloN- EhloL)procedure, respectively. The largest present double-!: bases yield much better numerical agreement, 11.16 and 9.01 eV, respectively; the values from 0 H a r e 8 are 10.10 and 9.75 eV, respectively, Torok et al.1° gave 9.81 and 9.00 eV, while the CNDO-S13 and Xa16 methods yield 5.48 and 8.3 eV (Koopmans' theorem only), respectively. When an unrestricted Hartree-Fock calculation was performed for the SN radical, with the largest basis set, the total energy was lowered to -451.926 83 au. The first IP then (31) Dyke, J. M.; Morris, A.; Trickle, I. R. J . Chem. Soc., Faraday Trans. 2 1977, 73, 147.
Findlay et al.
1310 Inorganic Chemistry, Vol. 19, No. 5, 1980 Table 11. Valence-Shell Orbital Energies (eV) for SN, S,N,, and S4N4(Selected Basis Sets)
Table IV. Ionization Energy Data (eV)and Assignments for S,N,
SN
3n 2ff 70 60 50
minimal spd
double f spd + midbond (largest)
11.78 12.78113.68 13.74 19.86 33.44
11.16 12.63/13.55 14.55 20.82 34.25
s*N, minimal spd
double f spd + 3 d+ ~ 3d, + midbond + center
11.25 10.34 10.95 13.61 16.31 18.21 17.67 19.00 27.06 30.20 38.00
10.59 10.62 12.21 12.87 16.93 16.96 18.03 19.59 27.18 30.45 37.09
2b3, Ibz, 4b3u 5bzu 7% 2blU 2% g 6% 4bzu 3b3u 5%
s4
N4 double f
minimal spd
spd
10.47 10.49 10.27 11.38 12.57 13.51 14.35 16.06 18.56 19.62 19.35 20.78 23.85 28.87 31.33 34.87 37.82
11.21 10.97 11.29 11.95 13.18 14.09 15.04 16.51 19.02 20.20 20.13 22.02 25.43 31.21 32.66 36.80 39.92
sp
+ midbond 10.63 10.71 10.93 11.72 12.87 13.49 14.60 16.12 18.53 19.56 19.94 21.55 24.94 30.32 32.02 35.75 38.66
Table 111. Ionization Energy Data (eV) and Assignments for S,N, IP assignt IP assignt 10.51 10.81 11.06 (sh) (12.17) 12.28d (12.39) (12.51)
2b3, 4b3u lb1'
I
..
14.42 16.77a 22.02b ~ 3 2
7ag, 2b, 2b1,, 6a, 4b,,, 3b3, ~ 5%
5b*"
a Value quoted by Frost et al." data.21 d Vertical.
He 11.
Estimate from XPS
became 9.72 eV (Koopmans' theorem) and 9.45 eV (ASCF). The dipole moment was slightly lower at 1.67 D (cf. 1.75 D). The virial ratio V / T was -1.999 89 and (Sz) 0.774; both are close to the Hartree-Fock values -2.00000 and 0.750, respectively. SzN2. The total energy, arising from the largest basis set calculation used here on SzN2,is the lowest yet reported (previous -903.7901 au9) for a single configuration study and comparatively close to the recent CI study by Jafri et a1.9 which yielded -903.913 87 au for the ground state. A survey of the earlier ab initio r e s ~ l t s ~shows ~ ~ ~that ' ~ ~the ' ~orbital energy levels in sequence by symmetry representation are far from
a
IP
assignt
IP
assignt
9.36 10.11 10.60 10.92 11.44 12.74 13.66
3a,, 8b,, 9a, 4b, 7b, lle 10e 9e 8al
15.27 16.93 20.4" 23.9" -28b -31 (35)b
6bz, 2a, 7% 8e 5b,, 3b, 7e 6a,
He 11.
Estimate from XPS data.I3
stable with respect to change of basis set. This is even more true if the semiempirical calculations6J'.-13 are compared. The present work set out to extend the range of total energy to see whether such a stability in order could be found. Our smallest basis set (minimal spd) yielded an order only different from the largest Jafri et aL9 set by a single interchange of orbitals. In the largest present basis a further change from the Jafri order was obtained, leading to the order (increasing binding energy) 2b3, (d< 1b2, (TN) < 4b3, (LPN) < 5'32, (LPd < 7a, (LPN/LPs) < 2bl, ( T ) . The magnitude of these shifts relative to our other large bases or the Jafri et al. order9 is small, and we regard the largest set as (effectively) having the Hartree-Fock limiting values. The relevance of these conclusions and the open-shell calculations to the photoelectron system is described below. First we discuss the UV-PE spectral appearance for SzN2with change of irradiation energy and then the comparison with earlier work. The He I photoelectron spectrum of SzNzobtained in the present work (Figure la) was in substantial agreement with that reported by Frost et a1.20although we were unable to obtain a spectrum entirely free of N2. This made it difficult to examine further the poorly resolved fine structure near 16 and 18 eV observed by Frost et al. The He I1 spectrum of S2N2(Figure Ib) revealed an additional weak band at 22-eV binding energy. Noticeable differences in appearance between the He I and He I1 spectra, after allowance for the larger slit width in the latter, were (a) a marked enhancement of the intensity of the fourth band relative to the third band (taking into account analyzer transmission differences) and (b) an obvious decline in the intensity of the first band at 10.5 eV relative lo the second at 10.8 eV under He I1 conditions. The first difference is discussed below, while the 10.5/10.8 eV change is consistent with a relatively high 3ps component in the 10.5-eV band and more 2pN in the 10.8-eV band. This is supported by known cross-section differences for S and N.32 Because of the substantial overlay between the He I and He I1 photoelectron spectra in our instrument, it is not usually practicable to observe IP's beyond 25 eV; thus bands associated with MO's of dominant Nb character are not located. A maximum of 5 out of the 11 valence-shell bands are accessible to us. The XPS spectrum of solid SzN2(at -100 " C ) under Mg Ka conditions shows groups of ionization maxima at 4.2, 7.0, 9.8, 15.8, and 25 eVZ1to high binding energy of the "instrument zero level". The highest binding energy peak must contain the N b levels, while the the four lower binding energy levels must be associated with the centroids of the groups of IP's in the UV-PES; these centroids are at 11.2, 14.4, 16.8, and 22 eV, yielding a linear shift between the two instrument scales of ca. 7 eV, this corresponds to the resultant of the Fermi level, charging effects, and work function. Thus the Nb levels of S2N2must lie near 32 eV in the gas phase; this is consistent with gas phase XPS data on N2 where the NZslevels are at 25.0 (u,) and 37.3 eV ( u g ) ,giving a mean value of 31 eV,33 ( 3 2 ) Schweig, A,; Thiel, W. J. Electron Spectrosc. 1974, 3, 27; J . Chem. Phys. 1974, 60, 951.
Inorganic Chemistry, VoZ. 19, No. 5, 1980 1311
Electronic Structure of the Sulfur Nitrides while pyrrole has Nzs at 29.5 eV (4a1)34etc. We thus have six main bands in which to identify 11 energy levels. The first band shows clear evidence of 3 IP’s. Intensity patterns in the He I1 spectra suggest that the third and fourth PE bands (near 14 and 17 eV) also relate to more than one ionization process. These are assigned to two IP’s in each case, yielding a final series of groupings (low to high binding energy) 3:1:2:2:2:1. This correlation is shown in Figure 3, together with energy levels calculated by various methods; the general level of sophistication of the calculations rises from left to right, and slight trends in orbital energy for a particular symmetry type have been utilized in the derivation of the final correlation. The experimental spectrum (Figure 1) shows four main IPS, and these can be correlated with groups of orbital energies (A, B, C, D; see Figure 3) from all calculations. The CNDO-211 and CNDO-S13 groupings do not appear to fit with the experimental intensity ratios above; the X a calculations6 are more satisfactory but do not separate groups A and B well; an arbitrary 6 eV has been added to these orbital energies to bring them near to the experimental range. The small ab initio basis sets7J5do not yield satisfactory A and B groupings. This is rectified in all of of the present calculations and in those of Jafri et aL9 None of the Koopmans’ theorem studies yields an internal 3:l ratio in group A, and in the largest basis-set calculations this arises from the LPN level (4b3,) being placed at too high a binding energy. Direct calculation of the first three ionization potentials for the largest basis set yields (EION - ITMoL) 9.33 (2b3,), 9.97 (lbzg), and 10.63 eV (4b3,), that is, three equally spaced IP’s, a result which is consistent with the broad envelope observed. Finally, we note the marked fine structure on the IP at 12.3 eV; this is calculated to be from 5bzU(LPs). We have noted that lone-pair sulfur levels in several heterocyclic compounds often show fine structure and contrast with the corresponding LPN; an example is 1,2,5thiadiazole (3) which shows well-defined structure on the LPs
c) 3
level assigned to the IP at 13.39 Overall, the assignment of the spectrum according to the large basis set of the present work seems satisfactory. Of the earlier methods only the X a calculations6 are of comparable utility. S4N4.The He I spectrum (Figure 2) is in good agreement with that of Salanek et al.13 whose spectral range was only 9-12 eV but contains four extra bands to higher energy; a further two IPS were observed under He I1 irradiation. Comparison of the latter spectrum with the solid-state X-ray photoemission spectrum of Salanek et al.13 indicates that the bands at 20.4 and 23.9 eV (He 11) correspond to maximma on the XPS profile at ca. 13- and 17-eV binding energy. This again leads to a scale shift of ca. 7 eV between the Fermi level and the UV-PES data. Thus the remaining inner-valenceshell ionizations are at ca. 28- and 35-eV (or possibly 31-eV) binding energy; the 35-eV choice seems more likely by comparison with S2N2and on a correlation of the calculated and experimental data below. These last two I P S lie beyond our observable range. We thus have a total of 13 distinct IP’s in the PE spectra. Of the 22 orbitals in the valence shell 10 orbitals form (33) Siegbahn, K.; Nordling, C.; Johansson, G.; Hedman, J.; Heden, P. F.; Hamrin, K.; Gelius, U.; Bergmark, T.; Werme, L. 0.;Manne, R.; Baer, Y. “ESCA Applied to Free Molecules,” North-Holland Publishing Co.: Amsterdam, 1969; p 64. (34) Gelius, U.; Allan, C. J.; Johansson, G.; Siegbahn, H.; Allison, D. A,; Siegbahn, K. Phys. Scr. 1971, 3, 237. (35) Heilbronner, E. In “Physical Methods in Heterocyclic Chemistry”; Katritzky, A. R., Ed. Academic Press: London, 1974; Vol. IV, p 1.
degenerate pairs, and so 17 distinct ionizations are anticipated. Comparison of the experimental IP’s with the canonical MO energies shows that the assignment is not trivial. A correlation, by symmetry, of the extended HUckel,l8J9 CNDO-S,13X q 6 and present ab initio calculations and a final correlation with the observed photoelectron spectrum are shown in Figure 4, with selected data in Table 11. The orbital energies of the Xa6 calculation were arbitrarily increased by 4 eV to bring them to the correct range. The orbital ordering of the EH and CNDO-S calculations is similar except for two marked changes of sequence of individual MO’s. Neither of these two calculations leads to reasonable groupings of MO’s or to the sequence of IP’s of gradually extending separation on moving to higher binding energy. This criterion is roughly fulfilled by the Xa6 and present ab initio calculations; there are however marked changes in order of orbitals in the lowbinding-energy sets, and the latter calculations seem more consistent with the experimental envelope. Furthermore, the ab initio results seem to settle toward particular groups as the number of basis functions is increased. Further useful guidance on the assignment was obtained from a comparison of the He I1 and He I intensity patterns and from changes in calculated orbital energy with basis set (below). We find (a) a marked decrease in intensity of the band at 13.7 eV on switching to He I1 excitation and (b) minor changes in the band profile near 10.9 eV. Earlier experimental and theoretical studies indicate that the SJPone-electron ionization cross section is markedly lower than that for NZp under He I1 irradiati~n.~’Detailed examination of the wave functions shows that extensive delocalization and mixing of N and S character occur in most orbitals. Notable exceptions are the two sulfur lone-pair orbitals (LP,) 8a1 and 7b2. The former (S1 Sz S3 S4) is almost pure sp hybrid, while the latter (Sl - S2 S3- S4) is almost pure S3p.incharacter. Similarly the two orbitals 9al and 4bl are of dominant nitrogen lone-pair character (LPN). Detailed population analyses are shown in the Tables V and IV. We expect therefore that intensities in the low-energy region of the He I1 spectra will largely reflect the number of distinct orbitals associated with each PE band, except that the structure related to the 8al and 7b2 levels should be anomalously weak. Finally we note the changes of calculated orbital energy with refinement of the basis set (Figure 4). The group of 4 orbital energies near 11 eV in the spbasis-set calculation with 56 functions clearly splits 3:l in the larger basis calculations (126). Slight respacing of the next group of 4 levels occurs. The two levels near 20 eV become nearly degenerate in the largest calculations. Finally open-shell calculations in the largest basis for the first three I P S (=&ON- &OL) yield the values 10.22 (2B2), 10.39 (’A2), and 10.84 eV (’A1), confirming the closeness of these ionizations. With these considerations in mind we arrive at the assignment shown in Figure 4 and Table 111. Particular support is then provided by (a) the marked diminution in intensity of the well-resolved IP at 13.7 eV with the switch from He I to He I1 excitation, a change consistent with the assignement to SLp@al) and (b) the change in groupings of IP’s with basis set to 9al, 3a2, 8b2 (corresponding to the first band) and 4bl, 7b2, 1l e (corresponding to the second group IP’s)
+ + + +
I
Discussion Molecular Energy Levels. Several features of the electronic structure of SzN2warrant discussion. With use of the above assignments, the splittings of symmetric and antisymmetric lone-pair combinations are 5.5 eV for LPN* and 4.5 eV for LP,*; in both cases the “normal” order LPx- is to lower binding energy (X = S, N). Both these values are extremely large and in part arise from the close geometric arrangement of atoms in planar S2N2. The structure has few direct
1312 Inorganic Chemistry, Vol. 19, No. 5, 1980
Findlay et al.
Table V. Mulliken Population Analyses for SN, S,N,, and S,N,
Table VI Mulliken Analysis for S,N, with Midbond and Center sp Functions
SN
1s + 2s + 3s 2Pu + 3Pu 2P, + 3P, 3ds midbond s Po P, total
%s
S
N
5.7778 2.6921 6.7552 0.0679
3.8306 1.2631 1.9735
2b,, lb,, 4b3, 5b,, 7ag 2b1, 2% g 6ag 4b,, 3b3, 5ag
...
0.4447 -0.0360 0.2311 15.6129 7.3871 SZN, largest basis
1s + 2s + 3s 2Pu + 3Pu 2P,+ 3P, 3dsPd~ midbond s Po P, center s Pn totala overlap pop. S-N
N
5.7369 5.6729 3.4984 0.1348
3.7326 2.3470 1.3139 0.0200
N-N
S,N, double 5 1s + 2s + 3s (2p + 3P)total 2 4 midbond S-S midbond S-N totala overlap pop. S-N
s-s
orbital 3s 8b, 3a, 9al 4b1 7b, lle 10e 9e 8a1
minimal spd N
S
N
5.7821 9.0127
3.6379 3.8054
5.6970 9.5294 0.3188
3.6066 3.8481 0
...
0.0412 0.3604 15.1964 7.8036 0.4135 0.3465 -0.0997
...
...
0 0 0 9 0 8 77 0 26 17 47 0 39 0 4 7 24 4 0 14 77 1 44 8
center
%s %p
%s %p
4 7 1 0 7 7 1 0 -1 -3 0
0 0 6 8
1 0 8 0 10 12 13
N
S
S
...
0 3 1 1 0 1 2 0 1 2 1
0 0 0 0 -1 0 0 0 0 0 1
0 0
-1 -2 0 2 0 0 -3 -1 0
...
...
15.5453 7.4547 0.3913 0.1248 -0.0251
N-N a Total populations include one-half of each midbond term for
all bonded atoms; in S,N, one-fourth of the center term is added to each atom.
analogies, but it is worth noting that the corresponding value for the LP,’ splittings in pyrazine (4) is 1.72 eV; there the
4
binding-energy order is reversed (ag < b2J, and this can be interpreted in terms of either “through-bond’’ coupling3s or perturbation by nitrogen36 of the benzenoid e2glevel. 1,4Dithiane (5)’ which is of course nonplanar, has a similarly
(11 5
(36) Palmer, M. H.; Gaskell, A. J.; Findlay, R. H. J . Chem. Soc., Perkin Trans. 2 1974, 178.
4 0 5 0 1 5 4 8 22
N
S ~~
~~
0.3461 -0.2471 -0.1257
s- s
% p % d %s % p
0 9 6 0 0 0 8 9 58 6 22 0 52 0 4 2 52 20 80 -1 12 0 29 5
midbond
Mulliken Analysis for S,N, on the Basis of Double-c Calculations
S
0.2092 0.0131 0.0619 0.0369 -0.1069 0.0201 15.3148 7.6852
-P*-
N
S
largest basis uhf
3p
2s
2p orbital 3s
3p
2s
2p
20 1 55 8 93 34 27 50 60
0 0 12 7 0 2 14 3 1
76 99 27 85 6 59 55 39 17
47 53 40 17 0 13 6 8
0 0 29 20 0 85 56 44
53 43 0 21 11 2 7 9
2a, 6b, 7a, 8e 5b, 3b1 7e 6a1
0 4 31 42 89 0 31 39
rationali~ed,~~ but much smaller, splitting for LPs of 0.45 eVa3’ Finally we draw attention to the near degeneracy ( A E = ca. 0.5 eV) of the two upper a levels in S2N2(1b2gand 2b3,) and the large separation (6 eV) from the inner a level (2b,,). This is reminiscent of the Huckel description of the a-isoelectronic valency shell of the cyclobuta-1,3-diene dianion (6). The latter
/01 6
has a degenerate (e”) subshell at E = 0 and a further a level (a;) at E = 2P. The 1b2gand 2b3, MO’s of S2N2are notable for the extreme degree of localization of the electron density on N and S , respectively. The D2d arrangement of S atoms in S4N4yields LPs combinations of al, e, and b2 symmetry. Our interpretation and calculations indicate the prevalence of the “natural” binding-energy (BE) order for the through-space interactions, namely, b, < e < a,. The close proximity of the S4 arrangement in S4N4to a tetrahedron is accompanied by the small separation of the e and b2 levels (AE = 0.5 eV from the IP’s), which would be degenerate (t) if Td symmetry prevailed. The two S4N4LP, levels 9al and 4bl mentioned above occur in the unexpected BE order 9al < 4bl (AE = 0.75 eV). This is comprehensible only in terms of limited mixing of the symmetric LPN and LPs group orbitals; the out-of-phase combination LP, - LPs is largely of N2pcharacter (85%) while the the in-phase combination LP, + LPs is of mixed Sjp(55%) and N2p(27%) character (Table VI). Direct comparison of S2Nzwith S4N4is of limited value owing to the very different geometric characteristics of the two compounds. The LPN levels at 10.8 (a) and 11.05 eV (a) in S2N2are close to the u values 9.36 (al) and 10.92 eV (b,) in S4N4;however, more marked differences are evident for LPs with values of 12.3 (b2,, in S2N2)and 10.6 eV (b, in S4N4), while the symmetric combination LPN LPs is at 16.8 eV
+
(37) Sweigart, D. A,; Turner, D. W. J . A m . Chem. SOC.1972, 94, 5599. Bock, H.; Wagner, G. Angew. Chem., Int. Ed. Engl. 1972, 11, 150.
Electronic Structure of the Sulfur Nitrides (7aJ in S2N2and 13.7 eV (sa,) in S4N4. Clearly the smaller ring size allows a more extensive interaction in S2Np;however, the classical representation of both molecules has the fragment -N-S-N-, and the lower binding energies deduced for the LPs levels in S4N4could derive in part from a weakening of the S-N linkage accompanied by S-S bonding, the change in electronegatively of the attached groups then being important. This is relevant to the localized MO study below. Few compounds possess structures analogous to S4N4,and it is difficult therefore to compare our 1 5 s with those for other molecules. One species containing a pseudotetrahedral array of sulfur atoms is the twist form of the tetramethyltetrathiane (7). The LPs levels for this molecule have been reported to
xx:x S
7
lie in the range 8.23-9.44 eV,38significantly lower than in S4N4;no doubt this is partially a result of “replacement” of the highly electronegative N by Me2C. The sulfur cage molecules As4S3and P4S3have lower IP’s than those found in the present study, namely, for As4S38.86 (al) and 9.31 eV (e) and for P4S3 9.24 (a,) and 9.57 eV (e).39 However, a clear identification of the nature of these IPSis awaited; if they originate in LPs, electronegativity differences are apparent, as well as an inversion of the expected order. The leading bands at IP’s of 9.4-10.19 eV in the UV-PES of S8 (D4d symmetry‘”’probably relate to differing nodal properties for this molecule; ab initio studies41suggest the order 3al E 3e3 < 3el = 3ez for the orbitals of lowest binding energy, at variance with the Xa-SW results.‘”’ Mulliken Analyses. The analysis of S2N2and S4N4,each for a single basis set, is given in Tables V and VI; the one chosen for S2N2is the largest used except that the 3dN polarization functions are absent, while the midbond (MB) and ring center (C) functions are included. The S2N2data show that the MB and C functions are utilized only to a small percentage in the occupied MOs. As a consequence the S4N4 data refer to the sp double-f basis only. Direct comparison of the present results for S2N2and S4N4with those from the Xa calculations6 is not easy since the analysis of the latter calculations records only the atomic s/p ratios for S and N rather than percentages of the total; thus it is not possible for most MO’s to tell whether the S / N ratio of populations is similar to those of the present work. The internal s/p ratios are comparatively similar for both S2N2and S4N4with the exception that the X a calculations seem to lead to much higher proportions of S3sin the levels at high binding energy. (It should be noted that the orbital numbering system in ref 6 refers to valence shell orbitals only.) A more direct comparison of the present wave functions for S4N4is with the CNDO-S results of Salanek et al.13 Except in those cases where the S/N proportions are controlled by symmetry, and hence in agreement, the present data (Table VI) are markedly different for most MOs. Furthermore, direct comparison of the individual MO compositions and the corresponding orbital energies shows that a change of ordering occurs within the three “e” orbitals in the center of the valence shell (9e-1 l e here, 3e-5e in ref 13). These extensive differences, confirmed by the schematic diagrams,13are somewhat surprising, since it is usually thought that the density function varies comparatively little with the (38) Guimon, M. F.; Guimon, C.: Metras, F.; Pfister-Guillouzo, G. J. Am. Chem. SOC.1976, 98, 2078. ( 3 9 ) Cannington, P. H.; Whitfield, H . J. J. Electron Spectrosc. 1977,10, 35. (40) Richardson, N. V.;Weinberger, P. J. Electron Specrrosc. 1975,6, 109. (41) Findlay, R. H. unpublished results.
Inorganic Chemistry, Vol. 19, No. 5, 1980 1313 method of calculating the wave function in high-symmetry molecules; i.e., a degree of topological control is usually thought to occur in the wave function. Total population analyses for SN, S2N2,and S4N4show a consistent pattern of behavior for a particular basis set, and the overall effect is donation of electron density for sulfur to nitrogen. In the cases of SN and S2N2both u- and ?r-donation mechanisms occur; a u/?r separation is not possible with S4N4. The 3ds orbitals appear to play a comparatively minor role although, as is usual, their inclusion has the effect of reducing the bond polarities. The polarization Nh-Sd+ is predicted to be similar in S4N4and S2N2and much larger than in S N itself. The values of the midbond function populations are always substantially larger than the 3ds or 3dNcomponents when these are added to the basis. Thus for SN’ the total (s p) midbond population is 0.885 e, of which almost half is the s function and the remainder largely T,/T : the p g component is actually negative (-0.08 e). The net ehect of these orbitals is to concentrate electron density in the central-bonding region rather than disperse it (negative populations). This is the reverse of the influence of atomic-centered 3ds or 3dN functions. The midbond functions play a rather smaller role in S2N2on a proportionate basis of four S N bonds; none-the-less the total (1.58 e) is large. By contrast, the center functions are much less important in S2N2. The ?r components of all the midbond and center terms are much smaller than the u functions. The center s function here is significantly negative (-0.13 e), thus reducing the electron density at the ring center and dispersing it back to the internuclear axes. When midbond S-N and S-S functions were inserted separately and then jointly into the double-f S4N4calculation, the resultant contributions were much larger in the S-N (0.36 e) than S-S bonds (0.08 e). As a test of variational as opposed to bonding effects, functions were placed near nitrogen but remote from the attached S atoms; these yielded a population of 0.06 e, Le., similar to those of the S-S midpoint functions. The mechanism of the S-S terms thus could be purely variational. However, an alternative possibility is that they are important only in the presence of polar S-N bonds. The possibility of cross-ring and cross-cage bonding is of course a matter of particular interest. The overlap populations for S2N2(Table V) clearly show that, while adjacent atoms are bonded (positive overlap), cross-ring bonding is absent, presumably as a result of the strong interactions between the opposing lone-pair electrons. The position for S4N4is somewhat different; here positive overlap populations are found for adjacent pairs of S atoms, albeit significantly smaller than those for adjacent pairs of S and N atoms. Localized Orbitals for S4N4and S2N2 Further insight into the bonding of these two molecules was obtained by transformation of the canonical wave function to a localized orbital basis (LMO) by using the Foster-Boys method42 which maximizes the sum of the squares of the distance between orbital centroids. For S4N4,four types of localized orbital emerge from the transformation, viz., S-N bonds (X8), S-S bonds (X2), LPs (X4), and LPN (x8). The degree of localization, showing the extent of two center Table VI1 character, is high except for the LPN orbitals; in these the remaining density is distributed among the four now nonequivalent S atoms, the major component being associated with the cis S atom, i.e. that closest to the LPN. In keeping with earlier semiempirical studies,” we find that the centroid (C) of the S-S bond orbital lies above the S-S
+
(42) Foster, J. M.; Boys, S.F. Reu. Mod. Phys. 1960, 32, 300. Boys, S. F. In “Quantum Theory of Atoms, Molecules and the Solid State”: Lowdin, P. O., Ed.; Academic Press: New York, 1966. Newton, M. D.; Switkes, E. J . Chem. Phys. 1971, 51, 3179.
Znorg. Chem. 1980, 19, 1314-1319
1314 Table VII. Localized MO’s for S4N4 and S,N,: Minimal spd Results s4
%localizn
3s
3p
3d
2s
2p
97.98 92.03 97.64 84.0
26.6 15.1 54.6 0
69.9 83.9 45.3 0
3.5 1.0 0.1 0
12.9 0 0 41.1
87.2 0 0 58.9
s*N, N
S
%localizn 3s S-N (X4) S-N(X2) LPS(IJ)A LPs(u)B LPs(“)*
97.8 96.5 98.5 98.3 92.9
21.3 11.7 64.5 62.5 0
N
-S
N
S
S-N (X8) S-S (X2) LPs (X4) LPN (X8)
I I1
Nu
3p
3d
2s
2p
74.8 85.2 35.5 37.5 99.6
3.9 3.1 0 0 0.4
26.0 15.4 0 0 0
74.0 84.6 0 0 0
axis but (in our hands) by only 0.06 A, corresponding to an angle SCS of 2.6’. Overall, therefore, and in agreement with the findings of ref 16, 17, and 19, we conclude that the molecule best fits the Lewis structure (8). The population analyses also show the
+
+ 8
tendency towards S+-N- character required by the classical structure (8). The valence-shell LMO’s of S2N2 show a number of characteristics in common with the features deduced from semiempirical studies,” although in the present work r and c MP’s were allowed to mix, thus leading to “bent” bonds rather than pure u or 7r LMO’s.” The final LMO wave function corresponds to the structure (9), Le., a single canonical form based on the pair resonance hybrids that can be drawn for a combination of S” and Sw bonding. The initial canonical
9
wave function is of course symmetrical, and the present form clearly shows the equivalence of the two S” and SIv centers. A consequence of this is that the two 17 LP, are not strictly identical since a u/7r separation has occurred at one side of the molecule and not at the other. The low level of delocalization of c LP, is reminiscent of the CNDO-2 wave function.11,’2 The absence of cross-ring bonding, as noted above from the negative overlap populations, is also confirmed. Concluding Remarks The earlier work on the photoelectron spectra of S2N2and S4N4has been extended by the measurement of the He I1 spectra. Detailed interpretation of the data for S4N4is difficult, but the new He I1 measurements, in conjunction with XPS data and the ab initio calculations by using more than one basis set, lead to a plausible interpretation for the complete valence-shell spectrum. This assignment differs significantly from that advanced on the basis of earlier semiempirical calculations. In contrast, the spectrum of S2N2is relatively straightforward in assignment. The present results are in substantial agreement with those of earlier work, except that the first IP is assigned to a r Srather than a rNlevel. A general feature emerging from the calculations, and consistent with the experimental photoelectron spectra, is that interactions among “lone-pair’’ orbitals are important in the sulfur nitrides. In the case of S2N2these lead to a very large “through-space” splitting of LPs* and LPN* levels. The situation in S4N4is more complicated, but the unexpected occurrence of the totally symmetric LPN level as one of the most weakly bound orbitals is best interpreted in terms of through-space interactions between symmetric LPs and LPN group orbitals. The conversion of our wave functions to a localized basis shows the absence of cross-ring N-N bonding and the presence of significant S-S bonding between each of the pairs of adjacent sulfur atoms in S4N4.By contrast, there is no cross-ring bonding in S2N2. Registry No. 1,28950-34-7; 2,25474-92-4; SN, 12033-56-6;SN’, 27954-72-9.
Contribution from the Inorganic Chemistry Laboratory, Oxford, OX1 3QR, Great Britain, and the Department of Chemistry, University of Edinburgh, Edinburgh, EH9 355, Great Britain
Electronic Structure of the Group 5 Oxides: Photoelectron Spectra and ab Initio Molecular Orbital Calculations RUSSELL G. EGDELL,* M. H. PALMER, and R. H. FINDLAY
Received July 30, 1979 Gas phase He I and He I1 photoelectron spectra of the group 5 oxides P406,As406,Sb406,and P4010are reported. Qualitative descriptions of the electronic structure of these molecules are discussed with reference to ab initio molecular orbital calculations for the species P4, P406,and P4Ol0. On the basis of the experimental and theoretical results, correlations among electronic energy levels within the series (i) P4, P406, and P40,0and (ii) P406,As406,and Sb406are suggested.
Introduction The group 5 oxides are introduced in many chemistry textbooks as prototype examples of cage inorganic structures.’ *To whom correspondence should be addressed at the Inorganic Chemistry Laboratory, Oxford.
0020-1669/80/1319-1314$01 .00/0
Recent interest in cage and cluster compounds has been stimulated by the belief that they may serve as molecular “models” for solid-state systems.2 ( 1 ) E.g.: Huheey, J. E. “Inorganic Chemistry”;Harper and Row: London,
1975. (2) E.g.: Muetterties, E. L. Science 1977, 196, 4292.
0 1980 American Chemical Society
